Abstract: A device in flexographic machines, for making an adjustment between an inner shaft and an extractable jacket, with the double purpose of supporting the jacket along the entire length of the shaft, and of increasing the stiffness of the jacket. The adapter comprises at each of its end portions a rigid ring, and these end rings are internally connected the one another by a first rigid cylindrical member which is thin and capable of expansion and is intended to rest against the shaft, and they are externally connected the one another by a second rigid cylindrical member intended to receive the jacket; expansion means are provided in order to secure said end rings to the shaft, and openings are provided in said second external member in order to allow blowing compressed air intended to make easier the insertion and the extraction of the jacket.